Discrete Fractional Difference Transform Method and its Application to Caputo-Gompertz Fractional Difference Equation

Source abstract

This study develops the Discrete Fractional Difference Transform Method (DFDTM) for the Caputo fractional difference based on the discrete fractional Taylor's formula. We establish theoretical properties of the method and apply it to the Gompertz fractional difference equation to model tumor growth dynamics. The interplay between the growth deceleration parameter and the fractional order is analyzed to investigate their effects on growth behaviour. The numerical convergence and truncation error analysis shows the DFDTM as a computationally efficient framework for simulating memory-dependent biological processes in discrete time. Furthermore, the Caputo Gompertz fractional difference model is employed to describe mammary tumor growth in rats, and its results are evaluated against the continuous Gompertz differential model using experimental tumor growth data.